How many 5 card poker hands consisting of 3 aces and 2 kings are possible with an ordinary 52-card deck?
Answer choice: a).12 b).288 c).6 d).24
I got 24 is that correct?
correct, did you get it by taking C(4,3)xC(4,2) ?
If so, good job.
To calculate the number of 5-card poker hands consisting of 3 aces and 2 kings, you can break down the problem into two parts: selecting the 3 aces and selecting the 2 kings.
Part 1: Selecting the 3 aces
There are 4 aces in a standard deck of 52 cards. To select 3 aces, you need to choose 3 out of the 4 aces. This can be done using the combination formula "nCr", where "n" is the total number of items to choose from and "r" is the number of items to choose. Therefore, the number of ways to select 3 aces is denoted as 4C3, which can be calculated as:
4C3 = 4! / (3! * (4-3)!) = 4
Part 2: Selecting the 2 kings
After selecting 3 aces, you are left with 2 kings to choose from. There are 4 kings in a standard deck, and you need to choose 2 out of the 4 kings. Similarly, you can calculate the number of ways to select 2 kings as:
4C2 = 4! / (2! * (4-2)!) = 6
Now, to get the total number of 5-card poker hands consisting of 3 aces and 2 kings, you multiply the results from Part 1 and Part 2 together:
4 * 6 = 24
Therefore, the correct answer is d) 24.
Based on your calculation of 24, it seems like you have correctly calculated the number of possible hands. Well done!